First principles calculations are used to establish that the electronic structure of graphene ribbons with zig-zag edges is unstable with respect to magnetic polarisation of the edge states. The magnetic interaction between edge states is found to be remarkably long ranged and intimately connected to the electronic structure of the ribbon. Various treatments of electronic exchange and correlation are used to examine the sensitivity of this result to details of the electron-electron interactions and the qualitative features are found to be independent of the details of the approximaton. The possibility of other stablisation mechanisms, such as charge ordering and a Peierls distortion, are explicitly considered and found to be unfavourable for ribbons of reasonable width. These results have direct implications for the control of the spin dependent conductance in graphitic nano-ribbons using suitably modulated magnetic fields.
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